solve the equation by completing the square. round to the nearest hundredth.

Question

x^2+10x=18

Answer 1

First, we need to rearrange the equation so that the constant term is on the right side:

x^2 + 10x - 18 = 0

To complete the square, we need to add and subtract (10/2)^2 = 25 to both sides:

x^2 + 10x + 25 - 25 - 18 = 0

Simplifying and factoring:

(x + 5)^2 - 43 = 0

Adding 43 to both sides:

(x + 5)^2 = 43

Taking the square root:

x + 5 = ±√43

Subtracting 5 from both sides:

x = -5 ± √43

Rounding to the nearest hundredth:

x ≈ -8.32 or x ≈ 2.32